Uniform Asymptotic Stability of Nonlinear Switched Systems With an Application to Mobile Robots

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Abstract
This paper is concerned with the study of, both local and global, uniform asymptotic stability for general nonlinear and time-varying switched systems. Two concepts of Lyapunov functions are introduced and used to establish uniform Lyapunov stability and uniform global stability. With the help of output functions, an almost bounded output energy condition and an output persistent excitation condition are then proposed and employed to guarantee uniform local and global asymptotic stability. Based on this result, a generalized version of Krasovskii-LaSalle theorem in time-varying switched systems is proposed. For switched systems with persistent dwell-time, the output persistent excitation condition is guaranteed to hold under a zero-state observability condition. It is shown that several existing results in past literature can be covered as special cases using the proposed criteria. Interestingly, as opposed to previous work, the main results of this paper are applicable to the situation where some switching systems are not asymptotically stable at the origin. The robust practical regulation problem of nonholonomic mobile robots is studied as a way of demonstrating the power of the proposed new criteria. A novel switching controller is proposed with guaranteed robustness to orientation error and unknown parameters in mobile robots.

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